フィボナッチ数

	--fibo: 定義そのままの素朴な再帰。
	fibo 0 = 0
	fibo 1 = 1
	fibo n = fibo (n - 1) + fibo (n - 2)
	f0 = 0:1:(zipWith (+) f0 (tail f0))
	--f1: f0をリスト内包表記に置き換えたもの。-XParallelListComp　オプションが必要
	f1 = 0:1:[x+y|x<-f1|y<-tail f1]
	--f2: mainは　f2 (0,1)
	f2 (a,b) = do
	print a
	f2 (b,a+b)
	--以下はState　Monadを利用したLoop。　Control.Monad.State　のインポートが必要。
	--f3: mainは　runStateT f3 (0,1)
	f3 :: StateT (Integer, Integer) IO b
	f3 = do
	(a,b) <- get
	liftIO $ print a
	put (b,a+b)
	f3
	--f4: mainは　runStateT f4 [1:0]
	f4 :: StateT [Integer] IO b
	f4 = do
	l@(a:b:c) <- get
	liftIO $ print l
	put $ (a+b):a:b:c
	f4
	--f5: mainは　runStateT f5 ([0,1], 0)
	f5 :: StateT ([Integer], Int) IO b
	f5 = do
	(l,i) <- get
	liftIO $ print l
	put (l ++ [(l!!i + l!!(i+1))],i+1)
	f5
	f6 :: [[Integer]]
	f6 = scanl (\x@(a:b:_) _ -> (a+b):x) [1,0] [0..]
	--f7 main = print "put 0" >> f7 1
	f7 :: Integer ->IO ()
	f7 b = do
	l <- getLine
	let a = read l
	putStr "put "
	print b
	f7 $ a + b

view raw fibo.hs hosted with ❤ by GitHub

---

f6 の実行例

*Main> last $ take 10 f6
[55,34,21,13,8,5,3,2,1,1,0]

これは

foldl (\x@(a:b:_) _ -> (a+b):x) [1,0] [0..８]

と同じです。

フィボナッチ数列の隣り合う 2 項の比は黄金比に収束^Wします。

	f2 (a,b) = do
	print (a,b)
	f2 (b,a+b)
	main = f2 (1,2)

view raw fibo2.hs hosted with ❤ by GitHub

	import Data.Ratio
	go = do
	c <- getLine
	let (a,b) = read c :: (Integer, Integer)
	print $ fromRational $ b % a
	go
	main = go

view raw gr.hs hosted with ❤ by GitHub

$ runghc fibo2.hs | runghc gr.hs

~
~
~
1.618033988749895
1.618033988749895
1.618033988749895
~
~
~
Ctrl-Cを押して終了。